Optimal smoothing in discrete-continuous linear and nonlinear systems

Abstract A receiver observes discrete noisy nonlinear samples of a continuous Gauss-Markov process. It is shown that a stable smoother can be realized as a cascade of two blocks: 1. (1) a discrete smoother producing discrete smoothed estimates and 2. (2) a continuous element reconstructing a continuous estimate. A remarkable invariance formula is shown to exist for the latter part. A few linear examples are considered illustrating the error variance dependence on important model parameters. A major point is that an analysis of the reconstruction problem is of importance not only for low sample rates but also for high input SNR.

[1]  Gerald Bierman.  Brief paper: An efficient fixed-lag smoothing algorithm for discrete linear systems , 1974 .

[2]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[3]  Someshwara C. Gupta,et al.  Discrete-time demodulation of continuous-time signals , 1972, IEEE Trans. Inf. Theory.

[4]  Thomas Kailath,et al.  Supplement to "a survey of data smoothing" , 1975, Autom..

[5]  John B. Moore,et al.  Fixed-lag demodulation of discrete noisy measurements of FM signals , 1973 .

[6]  T. Kailath,et al.  An innovations approach to least-squares estimation--Part III: Nonlinear estimation in white Gaussian noise , 1971 .

[7]  Aaron Weinberg,et al.  Digital Phase Lock for Optimum Demodulation , 1975, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[9]  John B. Moore,et al.  Discrete-time fixed-lag smoothing algorithms , 1973 .

[10]  Andrew P. Sage,et al.  Estimation theory with applications to communications and control , 1979 .

[11]  L. E. Zachrisson.  On optimal smoothing of continuous time Kalman processes , 1969, Inf. Sci..

[12]  Brian D. O. Anderson,et al.  On the stability of fixed-lag smoothing algorithms , 1971 .

[13]  A. K. Mahalanabis,et al.  Finite Lag Receivers for Analog Communication , 1975, IEEE Trans. Commun..

[14]  H. Kushner.  Introduction to stochastic control , 1971 .

[15]  G. Bierman.  Fixed interval smoothing with discrete measurements. , 1973 .

[16]  J. Meditch.  A survey of data smoothing for linear and nonlinear dynamic systems , 1973 .

[17]  Lennart Ljung,et al.  A unified approach to smoothing formulas , 1976, Autom..

[18]  Outline designs for stable continuous-time fixed-lag smoothers , 1972 .

[19]  Per Hedelin.  Can the zero-lag filter be a good smoother? , 1977, IEEE Trans. Inf. Theory.

[20]  John B. Moore,et al.  Fixed-lag smoothing for nonlinear systems with discrete measurements , 1973, Inf. Sci..

[21]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.